Closure operations are a useful device in both the theory and practice of tree reconstruction in biology and other areas of classification. These operations take a collection of trees (rooted or unrooted) that classify overlapping sets of objects at their leaves, and infer further tree-like relationships. In this paper we investigate closure operations on phylogenetic trees; both rooted and unrooted; as well as on X-splits, and in a general abstract setting. We derive a number of new results, particularly concerning the completeness (and incompleteness) and complexity of various types of closure rules. © 2006 Elsevier Inc. All rights reserved.
Grünewald, S., Steel, M., & Swenson, M. S. (2007). Closure operations in phylogenetics. Mathematical Biosciences, 208(2), 521–537. https://doi.org/10.1016/j.mbs.2006.11.005